This is an activity that can be done on the first day of school, with the preparation done before the students arrive.
Using two decks of cards, create enough pairs for each member of the class. Place one card of the pair on each desk, and keep the other card in a separate pile. After students come in, let each pick a card from your pile. They are then assigned to the corresponding desk.
Cheating is inevitable, and dissent is certain, but this is a random and ‘fair’ means of seating, with the students having opportunity to ‘choose’ their seat.